SINGAPORE (Reuters) - European and Asian airline shares mostly stabilised on Tuesday even as Dutch carrier KLM said it would suffer losses beyond its estimation from last week's terror attacks in the United States.

"Neither the longer-term consequences of the events in the United States nor the duration of such consequences can be fully envisaged at present," KLM Royal Dutch Airlines said in a statement.

"It is therefore currently impossible to estimate the magnitude of our full-year operating loss."

But there would be a loss, the airline said.

Investors looking at collapsed airline share prices decided enough was enough, and stocks from Tokyo to Paris began to show signs of stability.

U.S. airline shares crumbled on Monday, their first day of trading since the attacks, which have suppressed demand for air travel and have led to costly security measures that will further deter passengers and hobble airport capacity.

With aviation companies among the worst corporate victims of the attacks, a senior European Union finance official said the organisation may help affected sectors.

"If it's the case in the United States then it will be a problem also for the EU, so it will perhaps be necessary to do something," the chairman of the Eurogroup of euro-zone finance ministers, Didier Reynders, told the Financial Times newspaper in an interview.

The U.S. government is considering aid for its airlines.

BRITISH AIRWAYS, VIRGIN ATLANTIC TO MEET GOVERNMENT

The chiefs of British Airways Plc and Singapore Airlines (Singapore: SIAL.SI - news) Ltd affiliate Virgin Atlantic Airways Ltd prepared to meet the British government on Tuesday to discuss their security and finances.

Analysts believe that British carriers may have been particularly damaged by the attacks, because they rely more heavily on passenger and especially transatlantic traffic than other airlines.

The global economic slowdown evident before the terror attacks was already battering airlines' delicate profitability, which easily turns to loss due to thin margins, generally heavy debt loads and high fixed costs.

By 0755 GMT major airlines showed little overall price movement compared with their giant falls of the past week.

Japan Airlines Co Ltd <9201> was up three percent but Deutsche Lufthansa AG was down 4.8 percent.

Asian airlines said they had largely restored their U.S. services as of Tuesday, but some flights were still cancelled or being diverted.

Airlines flying into Sri Lanka were being asked to pay sharply higher war-risk premiums, a local official said. Premiums had already been hiked after a massive Tamil Tiger rebel attack on the country's main airport in July.

Japanese carriers, which resumed U.S. services on Sunday, have substantial exposure to the Americas but were unsure how hard they will be hit by the tragedy.

Second-ranked Japanese carrier All Nippon Airways Co Ltd <9202> said all flights were up and running, but tourist bookings had fallen.

Japan Airlines Co Ltd (JAL) <9201>, Japan's largest airline, said transpacific flights accounted for over a third of its international revenue in the year to March 31. But it said it had no immediate plans to change its earnings forecast.

Few airlines have given guidance to investors on their results, presumably because they can have no idea for some time of how they will trade over the coming year.

SINGAPORE AIRLINES SEES NO HIT TO BOOKINGS

One Asian carrier issued a surprising statement that almost suggested business as usual.

Singapore Airlines declined to detail revenue prospects but said bookings did not appear to be suffering from the attacks.

Anecdotes since the attacks and figures from reservations company Amadeus suggest widespread reluctance to fly.

Analysts say the industry took about a year after 1990-91 Gulf crisis to get back to its previous traffic volumes -- but that still implied an ongoing loss of business since airlines almost always expect rising passenger and freight operations from year to year, generally around five percent.